1. Topological aspects of incompressible flows.
- Author
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Bessa, Mário, Torres, Maria Joana, and Varandas, Paulo
- Subjects
- *
SHADOWING theorem (Mathematics) , *TOPOLOGICAL dynamics , *VECTOR fields , *GLUE , *POINT set theory , *INCOMPRESSIBLE flow - Abstract
In this article we approach some of the basic questions in topological dynamics, concerning periodic points, transitivity, the shadowing and the gluing orbit properties, in the context of C 0 incompressible flows generated by Lipschitz vector fields. We prove that a C 0 -generic incompressible and fixed-point free flow satisfies the periodic shadowing property, it is transitive and has a dense set of periodic points in the non-wandering set. In particular, a C 0 -generic fixed-point free incompressible flow satisfies the reparametrized gluing orbit property. We also prove that C 0 -generic incompressible flows satisfy the general density theorem and the weak shadowing property, moreover these are transitive. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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